Practical “Paritizing” of Emerson-Lei Automata

Abstract

We introduce a new algorithm that takes a Transition-based Emerson-Lei Automaton (TELA), that is, an ω-automaton whose acceptance condition is an arbitrary Boolean formula on sets of transitions to be seen infinitely or finitely often, and converts it into a Transition-based Parity Automaton (TPA). To reduce the size of the output TPA, the algorithm combines and optimizes two procedures based on a latest appearance record principle, and introduces a partial degeneralization. Our motivation is to use this algorithm to improve our LTL synthesis tool, where producing deterministic parity automata is an intermediate step.

Improvements to ltlsynt

“…All these transformations are performed on each SCC separately, and it may for instance happen that one SCC is paritized using CAR while another SCC is partially degeneralized to produce an acceptance condition that can be paritized with IAR. Our benchmarks performed on data from SYNTCOMP'17 suggest that the option --algo=lar often produces significantly smaller DPAs than --algo=lar.old [12].…”

“…The intent was to keep track of a smaller number of acceptance classes instead of colors, but this optimization was found to be incorrect during SYNTCOMP'19. This optimization was removed from Spot 2.8 for correctness sake, then replaced by many new optimizations in Spot 2.9 [12].…”

“…Option --algo=lar now triggers the new implementation of the paritization procedure [12]. It combines CAR (a generic transformation to parity) with IAR (a conversion of Rabin-like or Streett-like acceptance conditions to parity) as well as a partial-degeneralization (in order to reduce conjunctions of Inf or disjunctions of Fin that occur in the acceptance condition to a single term, as intended by the original symmetry-based optimization) and multiple simplifications of the acceptance conditions.…”

Stackelberg-Pareto Synthesis (Extended Version)

“…The following proposition describes how any objective in {B uchi, co-B uchi, Parity, Muller, Stree , Rabin} can be encoded into a Boolean Büchi objective such that a play satisfies the Boolean Büchi objective if and only if it satisfies the original objective. This encoding is standard and can be found for instance in [36]. We recall it for the sake of completeness.…”

“…Latest appearance records (LAR), which are structures that keep track of the most recently occurred vertices in a play, are often used in the literature. Modifications of these structures can be used to keep track of other values, such as the latest priorities occurring in a play [36]. We provide a modification on the LAR structure, called set appearance record (SAR), which, given a series of sets of vertices, keeps track of those most recently visited.…”